The following is a page index for Einstein's relativistic physics theory related terms. The terms as used on the pages are listed alphabeticaly. The page number that it appears on is listed and the link to that page number is named with an equivalent term on the right of the page number.


coordinate 29 acceleration, 61-62 coordinate acceleration, 93 coordinate frame acceleration, 107-108 acceleration according to the lab frame, 118-120 lab frame acceleration, 124-125 observer's acceleration, 163 ordinary acceleration, 174 acceleration according to the inertial frame, 176 frame's acceleration

four-vector 22 four-vector acceleration, 28 acceleration 4-vector, 52 vector acceleration, 54 tensor acceleration, 59-60 acceleration tensor, 116 acceleration vector

proper 29 proper acceleration, 59-61 proper frame acceleration, 72 invariant acceleration, 108 instantaneous rest frame

affine connections 48 Christoffel Symbols

Alcubierre warp drive 164-174 warp drive

Alcubierre-Broeck warp drive 166 Alcubierre, 174 Van Den Broeck

Bianchi identities 70 Bianchi, 75 Bianchi identities

big bang 89 big bang, 91 big bang universe

Birkoff theorem 141 Birkoff theorem

black hole

Schwarzschild 111-126 black hole, 137-141 Schwarzschild, 144-148 Schwarzschild black hole

Radiative Vaidya and Waite solutions 141 Vaidya

Reissner-Nordstrom 131 Reissner-Nordstrom, 136 charged black hole

Kerr 130 Kerr hole, 140 Kerr black hole

Kerr-Newman 127-135 Kerr-Newman, 140 Kerr-Newman black hole, 149 charged rotating black hole

Boyer-Lindquist coordinates 128 Boyer-Lindquist

Casimir effect negative energy effect, see energy negative Casimir

centrifugal pseudo-force see fictitious forces

charged black hole, see black hole Reissner-Nordstrom


charged rotating black hole, see black hole Kerr-Newman

Christoffel symbols, see affine connections

closed universe, see universe closed Vs open

comoving frames 71 comoving, 90 frame, 93 comoving frame

conservation of energy-momentum 65 conservation, 77-78 energy

conserved parameters of geodesic motion 65 conserved

coordinate velocity, see velocity coordinate

Coriolis pseudo-force see fictitious forces

cosmic string 136 cosmic string, radiating line of negligible mass and charge 141 radiating

cosmological constant 70-80 cosmological constant, 91 dark energy

covariant derivative 48-49 covariant derivative, 54 Christoffel symbols

critical mass for universe closure, see universe critical density of


Gaussian 67-68 curvature, 70 gaussian, 89-92 gaussian curvature

of the Universe, see universe negative curved, universe positive curved

Riemannian 45 Riemann curvature tensor, 68-70 Riemann curvature, 72-74 spacetime curvature

dark energy, see cosmological constant

dark matter 91 dark matter

deflection of light , see light deflection

Delta Kronecker, see Kronecker delta

density of matter in the universe 91-92 universe

divergence 78-79 divergence

domain wall 96 domain wall

Doppler shift 33-35 Doppler shift, 95 in modern physics

dot produce, see scalar product

Einstein field equations 75-80 field equations, 97 Einstein field equations, 104 for modern physics, 156 law of gravity

Einstein summation convention - Preface

Einstein-Rosen bridge 147 Einstein-Rosen bridge

Einstein tensor 76 Einstein tensor, 78 Einstein curvature tensor, 153-154 in Einstein's field equations, 178 Einstein's equations, 181 for physics

electrically charged rotating black hole, see black hole Kerr-Newman

energy in gravity waves 97 gravity waves, 100 gravity wave energy, 102-103 gravity energy tensor

energy-momentum conservation 78 momentum

energy-momentum four-vector 21 four-vector momentum, 23-24 momentum 4-vector, 27-30 momentum four-vector, 51-55 momentum vector, 57 vector momentum, 59-60 momentum tensor, 63 four momentum

energy negative

Casimir etc... 143-144 Casimir effect, 154 Casimir energy, 157 in physics, 164-165 Casimir, 167-169 in quantum mechanics, 171 negative energy, 173 exotic matter

gravitational field 109 gravitational field

equivalence principle

levels of equivalence 38-39 equivalence principle, 86 in theory

of gravitational and inertial mass 38 mass energy equivalence, 118 mass energy, 120-121 gravitational and inertial

ergosphere 130 ergosphere

Euclerian observer 171 Euclerian observer

Euclidean space , see spacetimes Euclidean

event 1 event, 5-6 event in spacetime, 8 event in relativity, 13-16 definition of an event, 25 for special relativity

event horizon 115-117 event horizon, 129-131 horizon, 136-138 Schwarzschild radius, 140 light can not escape, 145 point of no return, 154 black hole, 165 from general relativity, 169-170 caunchy horizon, 179 no escape

expansion of the universe 89-95 expansion of the universe, 180 universal expansion

faster than light (FTL) , see superluminal

fictitious forces see aslo gravitational pseudo-force

centrifugal 71 centrifugal, 80 fictitious force, 108 centrifugal force

Coriolis 80 coriolis force, 108 coriolis

transverse 80 transverse force, 108 transverse fictitious force

flat space 68 flat space, 92 flat spacetime


four-vector, see four-vector force

ordinary 27-29 force, 54 ordinary force, 84 Newton's 2nd law


acceleration, see acceleration four-vector

definition of 40 4-vector

force 22 four force, 27-28 4-force, 52 force four-vector, 54-55 force 4-vector, 57 4-vector force, 59 four-vector force, 60-63 force tensor, 84-85 tensor force, 87 four-force, 116 in modern physics, 118 for general relativity

momentum 23 four momentum, 27-29 4-momentum, 51-55 momentum four-vector, 57 momentum 4-vector, 59-60 4-vector momentum, 63 four-vector momentum

velocity 22-24 four velocity, 28 4-velocity, 30 velocity four-vector, 51-54, 57-62 velocity 4-vector, 72 4-vector velocity, 108 four-vector velocity, 116 for modern physics, 171 for general relativity

FTL (faster than light) , see superluminal

Galilean transformation equations 3 Galilean transformation

Gaussian curvature, see curvature Gaussian

general principle of relativity 39-40 principle of relativity

geodesic 56-58 geodesic motion, 107 geodesic equation, 131 geodesic, 147 shortest path through spacetime, 156 free fall acceleration, 172 acceleration due to gravity,

gravitational collapse 141 Oppenheimer-Snyder

gravitational field

as affine connections 182 affine connection

gravitational mass , see mass gravitational

gravitational pseudo-force 43 gravitational force, 72-73 gravity

gravitational potential 43 gravitational potential, 79 gravity potential, 104-109 gravitoelectromagnetism, 114 Schwarzschild gravitational potential, 182 gravity potential

gravity waves 97-103 gravity waves, 141 gravitational waves

Hawking radiation 137-141 Hawking Radiation

horizon, see event horizon

Hubble's "constant" 93-96 Hubble's constant

Hubble's law 93 Hubble's law

hypersurface 147 hypersurface

inertial frame 1 inertial frame, 8 inertial coordinate frame, 12-13 unaccelerated frame, 39 inertial frame observer, 64 Lorentz frame, 71 inertial observer frame

inertial mass, see mass inertial

inertial pseudo-force, see gravitational pseudo-force see also fictitious forces

inertia manipulation 143 inertia, 155-157 gravity drive

inner product, see scalar product

intrinsic curvature 42 spacetime curvature, 67-70 curvature tensor

invariant 16 invariant, 20 invariant scalar, 41 Lorentz invariant, 46-47 Lorentz scalar, 77 unchanged in coordinate transformation, 85-86 same for all observers

invariant mass, see mass invatiant

Kaluza-Klein theory 159-161 Kaluza-Klein

Kerr black hole , see black hole Kerr

Kerr-Newman black hole, see black hole Kerr-Newman

Killing vectors 65 Killing vector, 136 Killing field vector

Krasnikov tube 177-178 Krasnikov tube

Kronecker delta 44 delta Kronecker, 75 Kronecker delta, 98 delta, 108 Kronecker

Lagrangian 65 Lagrangian, 159 Lagrangian equation, 161 Lagrangian mechanics

lapse function 169 lapse function, 171 time lapse

Levi Chivita

e ijk 108 Levi Chivita

eablr 84 rank 4 Levi Chivita

light cone 15 light cone

light deflection in gravity field 63 deflection of light, 123-126 light in a gravitational field

light-like 17 light like

light speed 1 light speed, 123-124 speed of light, 163-164 speed c, 174-176 c speed

local 39 local, 45 local frame, 46 local to the observer, 55-56 special relativistic limit, 68 local free fall frame, 70 metric reduces to, 81 local transform

local free fall frame 39 free fall, 55-56 local free fall, 70 free fall observer

Lorentzian spacetime , see spacetimes Lorentzian

Lorentz guage 106 Lorentz guage

Lorentz transformation , see transformation Lorentz

Luxon 26 Luxon

Mach's principle 71-74 Mach's principle, 108 origin of inertia


gravitational 38 gravitational mass, 114 active gravitational mass, 118-121 gravitational charge, 143-144 gravitational source

inertial 22 inertial mass, 28-30 resistance to acceleration, 38 in Newton's second law, 59 passive gravitational mass, 118-121 resistance to deviation from geodesic motion

invariant 22 invariant mass, 28-30 rest mass, 52-53 mass, 59 rest energy

Maxwell's equations 83-85 Maxwell's equations

Mercury perihelion procession see perihelion procession

metric tensor 17 metric tensor, 42-48 metric, 129 invariant interval, 159-160 line element

Minkowski diagrams 11-15 Minkowski diagrams

Minkowski force 27-28 Minkowski force, 55 4-force

missing mass 91 dark matter

momentum conservation, see energy-momentum conservation

momentum four-vector, see energy-momentum four-vector

nagative curved universe, see universe negative Vs positive curved

negative energy, see energy negative

Neutrino tachyon candidates 26 tachyon

Newtonian limit 3 Newtonian limit, 26 low speed limit, 104-109 weak field

Newton's law of gravitation 38 Newton's law of gravitation, 104 law of gravity, 120 Newtonian gravitation

Newton's second law of motion 22 Newton's law of motion, 27-29 2nd law of motion, 52 Newton's 2nd law, 59-60 Newton's law

Noether theorem, 65 Noether theorem

open universe, see universe closed Vs open


pair production 137 pair production


length contraction 9 length contraction

grandfather 25-26 grandfather paradox, 152 time travel

twin 8 twin paradox

parallel transport 68-69 parallel transport

perihelion procession 115 procession

Planck units 183 Plank units

polarization of the vacuum 143-144 vacuum polarization

positive curved universe, see universe negative Vs positive curved

pressure in stress-energy tensor 76-77 pressure tensor, 81 energy tensor

principle of general covariance, see general principle of relativity

proper time as an invariant 16 proper time

Pythagorean theorem 16 Pythagorean theorem

quadrupole moment contribution to gravitational radiation 103 quadrupole moment

quantum ineguality 168 quantum inequality, 171-173 Pfenning-Ford

red shift

cosmological 93-95 cosmological red shift

in a Schwarzschild spacetime 122 Schwarzschild spacetime

velocity, see Doppler shift

Ricci scalar definition of 75 Ricci scalar

Ricci tensor definition of 75 Ricci tensor

Riemannian curvature definition of 68 Riemann curvature

Riemannian spacetime, see spacetimes Riemannian

Riemann tensor definition of 69 Riemann tensor

Reissner-Nordstrom black hole, see black hole Reissner-Nordstrom

Robertson-Walker model 89-96 Robertson-Walker

rotating black hole, see black hole Kerr

rotation parameter 127 rotation parameter

San Grasso 26 San Grasso

specific angular momentum 127 angular momentum

Schwarzschild black hole , see black hole Schwarzschild

Schwarzschild radius 114 Schwarzschild radius


Euclidean 45-46 Euclidean space

Lorentzian 45-46 Lorentzian spacetime

Riemannian 46 Riemannian spacetime

specific charge 127 charge

speed of light, see light speed

steady state universe 79 steady state

stress-energy tensor

of dust 52 energy tensor, 76 stress-energy tensor

of electromagnetic field 77 electromagnetic field energy

pseudo tensor for gravity waves 100 gravity waves

of massless fields 76-77 massless, 81 massless field

of perfect fluid 77 ideal fluid

string theories 159 string theory


true 177-179 superluminal, see also tachyon

false, but faster than c 163-176 faster than light, 179-181 faster than c

supernova 26 supernova

tachyon 25-26 tachyon

tardyon 26 tardyon

temperature of black holes 137-141 temperature

tensor calculus 17-20 tensor calculus, 40-49 tensor equation

tensor definitions of

contravariant and covariant 19 contravariant, 41 covariant

tidal gradient 71-74 tidal force

time travel 25-26 time travel, 151-155 time traveler


general global 41 frame transformation, 65 coordinate transformation

Lorentz 1-9 Lorentz transformation, 18-19 Lorentz transform, 31-33 Lorentz boost, 64 inertial frame transformation

Lorentz-like accelerated 7 accelerated transformation, 33 accelerated frame, 63-65 accelerated observer

transverse inertial force see fictitious forces

uncertainty principle 137 uncertainty principle

unification theories 158-161 unification theory


age of 90 age of the universe, 95 cosmological time

closed Vs open 91-92 closed curved

critical density of 91-92 critical density

expansion of 90 expansion of the universe, 93 universal expansion

negative Vs positive curved 91-92 positive curved

vacuum domain wall , see domain wall

vacuum polarization, see polarization of the vacuum

Van Den Broeck, Chris warp drive , see Alcubierre-Broeck warp drive


addition 29-31 velocity addition

coordinate 22 velocity, 30-31 coordinate velocity, 51 inertial frame velocity

four-vector, see four-vector velocity

warp drives 163-176 warp drive

white hole 146 white hole, 148 black hole time reversal

wormholes 123 wormhole, 144-152 Einstein-Rosen bridge