Who is Robert M Kerns?

Robert M Kerns Popular Books

Robert M Kerns Biography & Facts

In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically, so that no matter or non-gravitational fields are present. These are distinct from the electrovacuum solutions, which take into account the electromagnetic field in addition to the gravitational field. Vacuum solutions are also distinct from the lambdavacuum solutions, where the only term in the stress–energy tensor is the cosmological constant term (and thus, the lambdavacuums can be taken as cosmological models). More generally, a vacuum region in a Lorentzian manifold is a region in which the Einstein tensor vanishes. Vacuum solutions are a special case of the more general exact solutions in general relativity. Equivalent conditions It is a mathematical fact that the Einstein tensor vanishes if and only if the Ricci tensor vanishes. This follows from the fact that these two second rank tensors stand in a kind of dual relationship; they are the trace reverse of each other: G a b = R a b − R 2 g a b , R a b = G a b − G 2 g a b {\displaystyle G_{ab}=R_{ab}-{\frac {R}{2}}\,g_{ab},\;\;R_{ab}=G_{ab}-{\frac {G}{2}}\,g_{ab}} where the traces are R = R a a , G = G a a = − R {\displaystyle R={R^{a}}_{a},\;\;G={G^{a}}_{a}=-R} . A third equivalent condition follows from the Ricci decomposition of the Riemann curvature tensor as a sum of the Weyl curvature tensor plus terms built out of the Ricci tensor: the Weyl and Riemann tensors agree, R a b c d = C a b c d {\displaystyle R_{abcd}=C_{abcd}} , in some region if and only if it is a vacuum region. Gravitational energy Since T a b = 0 {\displaystyle T^{ab}=0} in a vacuum region, it might seem that according to general relativity, vacuum regions must contain no energy. But the gravitational field can do work, so we must expect the gravitational field itself to possess energy, and it does. However, determining the precise location of this gravitational field energy is technically problematical in general relativity, by its very nature of the clean separation into a universal gravitational interaction and "all the rest". The fact that the gravitational field itself possesses energy yields a way to understand the nonlinearity of the Einstein field equation: this gravitational field energy itself produces more gravity. This means that the gravitational field outside the Sun is a bit stronger according to general relativity than it is according to Newton's theory. Examples Well known examples of explicit vacuum solutions include: Minkowski spacetime (which describes empty space with no cosmological constant) Milne model (which is a model developed by E. A. Milne describing an empty universe which has no curvature) Schwarzschild vacuum (which describes the spacetime geometry around a spherical mass), Kerr vacuum (which describes the geometry around a rotating object), Taub–NUT vacuum (a famous counterexample describing the exterior gravitational field of an isolated object with strange properties), Kerns–Wild vacuum (Robert M. Kerns and Walter J. Wild 1982) (a Schwarzschild object immersed in an ambient "almost uniform" gravitational field), double Kerr vacuum (two Kerr objects sharing the same axis of rotation, but held apart by unphysical zero active mass "cables" going out to suspension points infinitely removed), Khan–Penrose vacuum (K. A. Khan and Roger Penrose 1971) (a simple colliding plane wave model), Oszváth–Schücking vacuum (the circularly polarized sinusoidal gravitational wave, another famous counterexample). Kasner metric (An anisotropic solution, used to study gravitational chaos in three or more dimensions).These all belong to one or more general families of solutions: the Weyl vacua (Hermann Weyl) (the family of all static vacuum solutions), the Beck vacua (Guido Beck 1925) (the family of all cylindrically symmetric nonrotating vacuum solutions), the Ernst vacua (Frederick J. Ernst 1968) (the family of all stationary axisymmetric vacuum solutions), the Ehlers vacua (Jürgen Ehlers) (the family of all cylindrically symmetric vacuum solutions), the Szekeres vacua (George Szekeres) (the family of all colliding gravitational plane wave models), the Gowdy vacua (Robert H. Gowdy) (cosmological models constructed using gravitational waves),Several of the families mentioned here, members of which are obtained by solving an appropriate linear or nonlinear, real or complex partial differential equation, turn out to be very closely related, in perhaps surprising ways. In addition to these, we also have the vacuum pp-wave spacetimes, which include the gravitational plane waves. See also Topological defectWhy is this here? How is it relevant to the topic? References H. Stephani, et al., "Exact solutions of Einstein's field equations" (2003) Cambridge University Press, 690 pages.. Discover the Robert M Kerns popular books. Find the top 100 most popular Robert M Kerns books.

Best Seller Robert M Kerns Books of December 2022

The Lost Siren e-book Download

The Lost Siren

Raven StormMay 16, 2022Get

A human female born into a breeding manor never has a choice…I am a slave, but at least I am alive. When the man with wings and scales gave me a second choice—I took it. I'll do what I m...

Little Women e-book Download

Little Women

Louisa May AlcottSeptember 29, 1868Get

An Apple Books Classic edition. Meet the Marches! Louisa May Alcott’s classic introduces us to four unforgettable sisters: beautiful Meg, tomboyish Jo, delicate Beth, and Amy, the indulged...

Dragon's Breath e-book Download

Dragon's Breath

Michael GordonJuly 8, 2019Get

What happens when a Dragon doesn't brush his teeth?  Well...We all heard about the ''dragon's breath''. That's why learning proper dental care is really important for a little boy and h...

Someone Else's Daughter e-book Download

Someone Else's Daughter

Linsey LanierOctober 29, 2010Get

Book I of the popular Miranda's Rights Mystery series by bestselling author Linsey Lanier.  A woman can never make herself too tough, too strong, or too street smart.  THE SEARCHIN...

Man In The Water e-book Download

Man In The Water

Jon HillOctober 5, 2021Get

An attempted murder. A missing spouse. And an international conspiracy that could change the world. Jack Green has always been skeptical of so-called facts. Though he's forced to confront th...

Explicit Erotic Sex Short Stories e-book Download

Explicit Erotic Sex Short Stories

Brenda BlanchardJanuary 5, 2021Get

Bestselling Erotica Author Brenda Blanchard Is Giving Away a Collection of Some of Her Best Work! "Explicit Erotic Sex Short Stories" by Brenda Blanchard gives you a sneak peek into the sedu...

Secrets and Scandals e-book Download

Secrets and Scandals

Piper GlendaleMay 5, 2022Get

Emily Delaney, a reporter for one of Hollywood’s hottest gossip magazines, has her world turned upside down when her former journalism mentor dies, and she is called back to the hometown s...

Let's Taco Bout It e-book Download

Let's Taco Bout It

Matthew RyanOctober 1, 2014Get

Mr Taco is feeling sad, it’s not easy being a little taco when everything around you is so BIG! Luckily, Patrick has a few ideas to help his friend... ————  NOT YOUR REGULAR S...

Falling for Prince Charming: A Feel-Good Romantic Comedy e-book Download

Falling for Prince Charming: A Feel-Good Romantic Comedy

Sophie-Leigh RobbinsSeptember 7, 2021Get

Falling for your best friend's brother is tricky… unless you're keeping it a secret. Elle I never thought I'd be serving hotdogs dressed as an actual hotdog at the local amusement park. No...

A Royal Farce e-book Download

A Royal Farce

Laura HeffernanNovember 23, 2021Get

A ROYAL FARCE is the hilarious first book in the Retail to Riches series, which follows a plucky big box store employee on her journey from fighting to pay the bills to discovering she’s m...

The Girl Outside: A Shocking and Gripping Psychological Thriller e-book Download

The Girl Outside: A Shocking and Gripping Psychological Thriller

James CaineJune 22, 2022Get

Her daughter has a dark secret. One that will turn their perfect small town upside down.  Now she's missing. Mandy Knox can't shake the gut wrenching feeling that something sinister hap...

Lola Is Missing e-book Download

Lola Is Missing

Alison JamesFebruary 7, 2018Get

‘I was hooked from page one and couldn’t put it down until I’d reached the end. The twists and turns just keep coming … will have you gasping in surprise.’  Goodreads Reviewer...

Persuasion e-book Download

Persuasion

Jane AustenJune 16, 2020Get

Persuasion was published in 1817, six months after Jane Austen’s death, and is the last novel she completed in full. The novel tells the story of Anne Elliot, now in her late 20s, the daug...

The Baltic Run e-book Download

The Baltic Run

Charles WhitingJune 15, 2020Get

From the carnage of war a new hero is born. 1920. The slaughter of World War One is over, but already secret little wars are breaking out all over 'New Europe'. Sub-Lieutenant de Vere Smith ...

The Recruiting Trip e-book Download

The Recruiting Trip

Lexy TimmsNovember 19, 2014Get

Aspiring college athlete Aileen Nessa is finding the recruiting process beyond daunting. Being ranked #10 in the world for the 100m hurdles at the age of eighteen is not a fluke, even though...

Wanna Puck? (Book Two) e-book Download

Wanna Puck? (Book Two)

Layla Valentine & Ana SparksDecember 24, 2021Get

One cool-as-ice veteran player One smoking hot rising star And little old me in the middle All wrapped up in an all-star ménage a trois I've been sent to write a piece on two NHL stars Joel...

Contract with a SEAL e-book Download

Contract with a SEAL

Kate AsterSeptember 7, 2016Get

Some contracts are meant to be broken... Desperate to shake herself free from the humiliation of a very public divorce, TV financial correspondent Vi Owens makes a deal with a Navy SEAL Comm...

The Wonderful Wizard of Oz e-book Download

The Wonderful Wizard of Oz

L. Frank BaumMay 17, 1900Get

An Apple Books Classic edition. You’ve seen the iconic 1939 movie, but do you know about the talking field mice, the Winkies, and the Witch of the North that appear in the original book? L...

The Bangover e-book Download

The Bangover

Lili ValenteOctober 3, 2019Get

Note to Self --Do NOT bang your best guy friend in the limo on the way to the swanky Vegas hotel. I give myself very good advice. Too bad I suck at taking it. If only Colin and I hadn't ...

Croc's Return e-book Download

Croc's Return

Eve LanglaisDecember 3, 2015Get

Welcome to Bitten Point, where the swamp doesn't just keep its secrets, it sometimes eats them. Take one deadly bite and, bam, a man's life is changed forever, or so Caleb discovers when a l...

Without Mercy (A Dakota Steele FBI Suspense Thriller—Book 1) e-book Download

Without Mercy (A Dakota Steele FBI Suspense Thriller—Book 1)

Ava StrongJune 14, 2022Get

MMA champ-turned-FBI Special Agent and BAU specialist Dakota Steele is as tough as they come—and as brilliant, too, able to crack serial killers that no one else can. But this new case is ...

A Lot Like Home e-book Download

A Lot Like Home

Kathryn CantrellMay 21, 2018Get

Destiny isn't a thing in her world. Smooth-talking strangers need not apply... Superstition Springs native Havana Nixon is convinced letting a big developer into their tiny Texas oasis is th...

Don't Play With Odin e-book Download

Don't Play With Odin

Cynthia EdenJuly 13, 2021Get

Big, bad, and currently out of his element... Odin Shaw thought he’d spend his life on a battlefield. But fate had other plans, and now the former Special Forces operative has just landed ...

My Always One e-book Download

My Always One

Aleatha RomigJuly 27, 2021Get

MY ALWAYS ONE:  Friends to lovers stand alone When we were young, Samantha Anderson was the girl down the street. For as long as I remember, she’s been my partner in crime, in adventu...

High Conflict e-book Download

High Conflict

Amanda RipleyApril 6, 2021Get

When we are baffled by the insanity of the “other side”—in our politics, at work, or at home—it’s because we aren’t seeing how the conflict itself has taken over. That’s what ...

Stop Procrastinating & Overthinking: Learn The Mind Hacks To Cure Your Procrastination Habit And Improve Your Perseverance To Overcome Laziness. Eliminate Negative Thoughts And Stop Worrying e-book Download

Stop Procrastinating & Overthinking: Learn The Mind Hacks To Cure Your Procrastination Habit And Improve Your Perseverance To Overcome Laziness. Eliminate Negative Thoughts And Stop Worrying

Sebastian GoodwinMarch 25, 2021Get

"I TRIED EVERYTHING ELSE, BUT IT'S STILL A NEVER-ENDING BATTLE…" Everybody knows that procrastination is the biggest waste of time – I am talking about those moments when you imagine wha...

Make Me Wilder e-book Download

Make Me Wilder

Serena BellMay 20, 2021Get

She's a city girl. I'm a mountain man. This shouldn't work. So why can't I stay away? Gabe: I promised my dad I’d take care of the Wilder family adventure business, including my rowdy co-w...

Let's Talk About Hard Things e-book Download

Let's Talk About Hard Things

Anna SaleMay 4, 2021Get

From the host of the popular WNYC podcast Death, Sex, & Money , Let’s Talk About Hard Things is “like a good conversation with a friend” ( The New Yorker ) where “no topic is off...

Small Town Big Rumors e-book Download

Small Town Big Rumors

Willow WintersFebruary 8, 2022Get

He tasted like tequila and the fake name I gave him was Rose. Four years ago, I decided to get over one man, by getting under another. A single night and nothing more. I found my handsome st...

Mr. Nice Guy e-book Download

Mr. Nice Guy

Belinda WilliamsJune 28, 2021Get

NICE GUYS CAN PLAY DIRTY TOO . . . 'Give me a week. Seven days and seven nights. I'll show you what it's like to be with a nice guy.' Chelsea's housemate Tom is tired of her complaining abou...

Apple Watch User Guide e-book Download

Apple Watch User Guide

Apple Inc.September 16, 2021Get

Here’s everything you need to know about Apple Watch and the Apple Watch app on iPhone, straight from Apple. This definitive guide helps you get started using Apple Watch with watchOS 8 an...

iPad User Guide e-book Download

iPad User Guide

Apple Inc.September 20, 2021Get

Here’s everything you need to know about iPad, straight from Apple. This definitive guide helps you get started using iPad with iPadOS 15 and discover all the amazing things it can do.

Love Me Like a Love Song e-book Download

Love Me Like a Love Song

Annmarie BoyleNovember 9, 2020Get

She used to be on top of the music world. He's desperate to get there. Unable to compose since the death of her rock star husband, Grammy award-winning songwriter, Grace O'Connor is terrifie...

Bedtime Stories for Kids e-book Download

Bedtime Stories for Kids

Uncle AmonJune 15, 2015Get

Are you looking for a children's book that is highly entertaining, great for early readers, and is jam-packed with bedtime stories? This children's storybook has it all! This is an excellent...

Smitten with Ravioli e-book Download

Smitten with Ravioli

Ellen JacobsonMay 22, 2020Get

I'm not sure what I'm more scared of—cats that drool or falling for that annoying history professor in my Italian cooking course. Sure, Preston Whitaker has amazing blue eyes, but he's an ...

Jaxon e-book Download

Jaxon

Olivia SandsJune 2, 2019Get

She's his little sister's best friend.  Completely off limits.  And now they're working together. Jaxon Green 's plans to offer a summer camp for kids at his thoroughbred training ...

Some Call It Love e-book Download

Some Call It Love

Sarah PeisAugust 20, 2018Get

"The best feel-good romcom you need right now." Goodreads reviewer A mistaken arrest, an unpaid debt, and a trip to Vegas. Living in a small town where everyone knows your business isn't eas...

Liberty Begins e-book Download

Liberty Begins

Leigh JamesFebruary 13, 2015Get

Adventure. Fate. From Rags to Riches… My name is Liberty and I'm a good girl. I come from nothing. I have no one but myself. Sometimes I do things I don't want to -- I do them beca...

Savage Prince e-book Download

Savage Prince

Meghan MarchApril 24, 2018Get

Who knew things could get even darker and dirtier in New Orleans?  New York Times  bestselling author Meghan March introduces the  Savage Prince  of the city, the man you...

Accidentally Aphrodite e-book Download

Accidentally Aphrodite

Dakota CassidySeptember 24, 2019Get

An apple a day keeps the Goddess in play... Mythology buff Quinn Morris has always wanted to visit Greece, where her inner hardcore romantic envisioned proposing to her boyfriend. And she's ...

iPhone User Guide e-book Download

iPhone User Guide

Apple Inc.September 20, 2021Get

Here’s everything you need to know about iPhone, straight from Apple. This definitive guide helps you get started using iPhone with iOS 15 and discover all the amazing things it can do.

Today I Am Mad e-book Download

Today I Am Mad

Michael GordonSeptember 7, 2020Get

Kids feel emotions in big ways! Here's a great story for helping kids manage their feelings. * Help children learn to identify and regulate their ...

Coming Home to Glendale Hall e-book Download

Coming Home to Glendale Hall

Victoria WaltersSeptember 25, 2019Get

'WOW! From the first page I was absolutely hooked ...Would highly recommend to get you in a feel good mood!’ (5 stars) Netgalley reviewer Uplifting and full of heart - this is an utter tre...

The Art of War e-book Download

The Art of War

Sun TzuOctober 4, 2010Get

An Apple Books Classic edition. It’s believed that Sun Tzu wrote this Chinese military primer during the 5th century BC-hundreds of years before the Bible. The book’s 13 chapters explore...

Her Dream Cowboy e-book Download

Her Dream Cowboy

Laura AnnMay 9, 2022Get

She's fulfilling her mother's dying dream, he's leaving his legacy behind... When their paths cross, can they find love despite going in different directions? Scarlett Dylan was raised in th...

Girl, Alone (An Ella Dark FBI Suspense Thriller—Book 1) e-book Download

Girl, Alone (An Ella Dark FBI Suspense Thriller—Book 1)

Blake PierceDecember 16, 2020Get

FBI Agent Ella Dark has studied serial killers from the time she could read, devastated by the murder of her own sister. With her photographic memory, she has obtained an encyclopedic knowle...

Lost Souls e-book Download

Lost Souls

W.J. MayNovember 22, 2018Get

Your curse is your biggest strength. I just didn't know it yet. Jamie Hunt's the high school quarterback in his senior year. He's popular, smart, got the prettiest girl in the school chasing...

The School of Starting Over e-book Download

The School of Starting Over

Lisa SwiftMarch 11, 2020Get

‘this was a delight to read …I just can’t recommend it enough. The best romance book I’ve read this year .’ ☆☆☆☆☆ Books and Bookends Nell’s going back to school… but ...

Hook e-book Download

Hook

Chelle BlissJanuary 15, 2019Get

Falling in love is supposed to be the easy part. But nothing prepared me for losing my wife. I promised her that I’d love again. Find someone to mend my broken heart. And that seems imposs...

Man Crush Monday e-book Download

Man Crush Monday

Kirsty MoseleyFebruary 3, 2020Get

Perma-single Amy Clarke prides herself on three things: her pink hair, her Converse collection, and her ability to drink copious amounts of margarita without puking. She isn’t looking for ...

Best Seller Robert M Kerns Audio Books of December 2022

The Laws of Human Nature (Unabridged) audiobook
The Laws of Human Nature (Unabridged)Robert Greene$16.99

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Think and Grow Rich audiobook
Think and Grow RichNapoleon Hill$14.99

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Untamed (Unabridged) audiobook
Untamed (Unabridged)Glennon Doyle$16.99

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The 5 Love Languages audiobook
The 5 Love LanguagesGary Chapman$16.99

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The Seven Husbands of Evelyn Hugo (Unabridged) audiobook
The Seven Husbands of Evelyn Hugo (Unabridged)Taylor Jenkins Reid$16.99

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Can't Hurt Me: Master Your Mind and Defy the Odds (Unabridged) audiobook
Can't Hurt Me: Master Your Mind and Defy the Odds (Unabridged)David Goggins$21.99

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The Obstacle Is the Way: The Timeless Art of Turning Trials into Triumph (Unabridged) audiobook
The Obstacle Is the Way: The Timeless Art of Turning Trials into Triumph (Unabridged)Ryan Holiday$12.99

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The Fellowship of the Ring audiobook
The Fellowship of the RingJ.R.R. Tolkien$19.99

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Rising Tiger (Unabridged) audiobook
Rising Tiger (Unabridged)Brad Thor$14.99

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The 6:20 Man audiobook
The 6:20 ManDavid Baldacci$16.99

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Greenlights (Unabridged) audiobook
Greenlights (Unabridged)Matthew McConaughey$14.99

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The It Girl (Unabridged) audiobook
The It Girl (Unabridged)Ruth Ware$14.99

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The Untethered Soul: The Journey Beyond Yourself audiobook
The Untethered Soul: The Journey Beyond YourselfMichael A. Singer$12.99

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Harry Potter and the Prisoner of Azkaban audiobook
Harry Potter and the Prisoner of AzkabanJ.K. Rowling$25.99

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Harry Potter and the Sorcerer's Stone audiobook
Harry Potter and the Sorcerer's StoneJ.K. Rowling$8.99

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Scars and Stripes (Unabridged) audiobook
Scars and Stripes (Unabridged)Tim Kennedy$16.99

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Harry Potter and the Chamber of Secrets audiobook
Harry Potter and the Chamber of SecretsJ.K. Rowling$8.99

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How To Win Friends And Influence People (Unabridged) audiobook
How To Win Friends And Influence People (Unabridged)Dale Carnegie$14.99

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The Girl Upstairs audiobook
The Girl UpstairsGeorgina Lees$2.99

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We'll Always Have Summer audiobook
We'll Always Have SummerJenny Han$16.99

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A Court of Thorns and Roses audiobook
A Court of Thorns and RosesSarah J. Maas$22.99

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One of Us Is Dead audiobook
One of Us Is DeadJeneva Rose$3.99

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Reminders of Him: A Novel (Unabridged) audiobook
Reminders of Him: A Novel (Unabridged)Colleen Hoover$25.99

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Endure audiobook
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True Believer (Unabridged) audiobook
True Believer (Unabridged)Jack Carr$16.99

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The Wrong Side of Goodbye audiobook
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The Power of Now: A Guide to Spiritual Enlightenment audiobook
The Power of Now: A Guide to Spiritual EnlightenmentEckhart Tolle$19.99

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It Ends with Us (Unabridged) audiobook
It Ends with Us (Unabridged)Colleen Hoover$12.99

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They Want to Kill Americans audiobook
They Want to Kill AmericansMalcolm Nance$19.99

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Good to Great audiobook
Good to GreatJim Collins$19.99

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