General relativity is about gravity {gravitation, relativity}| and accelerations. For small gravity, observers calculate that gravitation and acceleration have the same local effects on space-time curvature. Because gravitational field strength varies inversely with distance, observers calculate that gravitation and acceleration have different global effects on space-time curvature.
time
Because stationary observers calculate that gravity rotates space-time time and radial-space coordinates toward each other, clocks in gravitational fields, or undergoing accelerations, run slower. People age slightly more quickly on Moon than on Earth, because Moon has smaller gravitational field. People age more slowly on accelerating rockets than on Earth.
object length
Observers calculate that accelerating massive objects decrease length. After accelerating finishes, observers calculate that length returns to previous amount.
object mass
Observers calculate that accelerating massive objects increase mass. However, mass increase increases inertia and resists further acceleration. After accelerating finishes, observers calculate that mass returns to previous amount.
energy
Gravity depends on mass, directed potential energy, directed kinetic energy, and random-energy temperature. Mass and random energy are always positive. Gravity fields cannot cancel, because they are only positive. Because gravity is infinite and is only positive, gravity can have unlimited energy amounts.
sources
General-relativity stress-energy tensor has ten independent gravitational-field sources and ten independent internal-stress sources. Sources all conserve energy and momenta. Field equations are d'Alembert potential equations.
physical-law invariance
Gravitation and acceleration curve space-time, so non-locally physical laws vary under coordinate transformations.
uncertainty principle
Gravitational-field values correspond to position. Field-value-change rates correspond to momenta. Therefore, uncertainty principle applies to gravitational-field values and value-change rates.
black holes
Because gravity is unlimited, gravity can become strong enough to overcome all object accelerations, so even light cannot escape the space region. Outgoing geodesics converge. Space curves so much that it closes on itself, forming a region separate from space-time, not observable from outside. Only gravity can cause space-time singularities, because it is never negative.
gravitational entropy
Spaces have entropy that depends on topology (Euler number). Gravity curves space-time and creates different topologies, so gravity has entropy. Because only gravity is always positive, only gravity has entropy. Other forces cannot curve space-time, because they are not infinite and/or are both positive and negative.
gravitational entropy: black hole
Because gravity has entropy and forms black holes, black holes trap entropy. Black-hole trapping amount depends on event-horizon radius, so black-hole entropy depends on event-horizon spatial area.
Because black holes have entropy, they have surface temperature at event horizon. At event horizon, virtual-particle creation can allow one virtual-pair member to tunnel through event horizon to space, causing black hole to lose matter and eventually dissipate. Entropy decreases, rather than always increasing. Black holes disrupt quantum-state deterministic development and mix states {mixed quantum state}.
repulsion
Perhaps, gravity can temporarily repulse, and cause universe origin. Exotic particles can have negative pressure, causing repulsion. Larger spaces have more repulsion because pressure is in space, not in ordinary particles.
Objects with mass have gravitational forces {gravitational pressure} on top, bottom, middle, and sides, all pointing toward mass center. See Figure 1.
Imagine that object is fluid. Gravitation pulls all points straight down toward mass center. Pull is directly proportional to mass m and inversely proportional to distance r squared: m / r^2. Pull is least at farthest points least and most at nearest points.
Volume reduction changes mass density and energy density, and so changes pressure. Gravity tends to reduce volume, and increase pressure, until outward pressure force per area balances inward gravitation force per area.
Gravitational-field accelerations make waves {gravity wave}| {gravitational wave}. Gravitational waves make space-time curvature oscillate in two dimensions.
speed
Gravitational waves travel at light speed.
frequency
Gravitational-wave frequencies are about 1000 Hz.
medium
Gravitational waves oscillate gravitational-field surfaces. Gravity waves need no other medium.
quadrupoles
Gravity waves have two orthogonal linear-polarization states, at 45-degree angle, making field surfaces (not just lines). Gravity waves are quadrupole radiation. Because mass can only be positive (unlike electromagnetic positive and negative charges), no mass-dipole or gravitational-dipole radiation can exist.
At peaks, potential energy is maximum, and kinetic energy is minimum. As they pass, gravitational waves stretch and compress (vibrate) objects with mass.
spin
Gravitational waves can rotate. Primordial gravitational waves have different spin {polarization, gravity} than current ones.
graviton
Gravitational-force exchange particles are gravitons and have no mass. Gravitons have spin 2, which is invariant under 180-degree rotation around motion direction.
sources
Gravity waves come from oscillating and/or accelerating masses, such as pulsating stars, irregularly rotating stars, collapsing stars, exploding stars, or interacting star clusters.
superposition
Because masses are always positive, gravitational fields cannot cancel each other. However, locally, accelerations and/or decelerations can cancel gravitational fields. Because gravitational waves are non-local and have components in more than one direction, and accelerations are in only one direction, accelerations and/or decelerations cannot cancel gravitational waves.
comparison with electromagnetic waves
Gravitational fields have advanced and retarded solutions and their equations are similar to those for electromagnetic waves.
renormalization
Gravitational waves are infinite and require renormalization for gravitational-wave calculations.
Pressure measures momentum exchange. System external pressure puts force per area on system-boundary surfaces. It is due to kinetic energy, which increases with temperature.
internal pressure
System internal pressure {internal pressure}| puts force per area on system particles. It measures system potential energy changes as system expands or contracts while keeping temperature constant. Internal pressure is positive for attractive forces and negative for repulsive forces.
Vacuum has no forces, so its internal pressure is zero. Particles have no internal forces, so their internal pressure is zero. Solids have attractive forces, but particle distances do not change at constant temperature, so internal pressure is zero.
positive internal pressure
Gas particles slightly attract, and system volume can change at constant temperature, so particle distances can change at constant temperature, and gases can have positive internal pressure. Hotter gases push particles farther apart against attractive forces, increasing positive potential energy, so hotter gases have more internal pressure than cooler gases. Photons have radiation pressure that pushes against electromagnetic forces, increasing positive potential energy, so photon "gases" have positive internal pressure.
negative internal pressure
Systems that have internal repulsive (negative) forces have negative potential energy and negative internal pressure. For example, if external force compresses rubber membranes, rubber has repulsive forces that tend to push particles apart. The internal restoring force is negative, so internal potential energy is negative, with negative internal pressure.
gravity
At space-time points, gravity G depends on mass-energy density M and on internal pressure P: G ~ M + 3 * P. Hotter gas has more positive internal pressure than cooler gas and so more positive gravity. Photon "gas" has positive internal pressure that is one-third of energy density, so gravity doubles: M + 3 * (M/3) = 2 * M.
Quantum vacuum has negative (repulsive) force that expands space, increasing negative potential energy (dark energy) by subtracting universe positive kinetic energy, and so cooling the universe. Quantum vacuum has negative internal pressure between one-third and one of mass-energy density, so repulsive antigravity is between zero and negative two times mass-energy density: M + 3 * -(M/3) = 0 and M + 3 * (-M) = -2*M.
Gravitational fields have different strengths at different distances from mass-energy. In gravitational fields, objects have different forces {tidal force} on side nearest to mass-energy, side farthest from mass-energy, and middle. Tidal distortions depend on gravitational-field strengths at different space points.
Gravity varies inversely with distance squared {inverse square law}, so tidal effects vary inversely with distance cubed (by integration). Therefore, tidal effects can measure gravitational-field strength.
See Figure 1. The larger object is denser and has much more mass than smaller object. The smaller object is fluid. The objects are not far apart.
near and far
Gravitation pulls smaller-object nearer side, farther side, and middle straight toward larger-mass center. Nearer side feels strongest gravity, and its particles accelerate most. Middle feels intermediate gravity, and its particles accelerate intermediate amount. Farther side feels weakest gravity, and its particles accelerate least. Along vertical, small object tends to stretch out from middle, keeping same volume.
left and right
Gravitation pulls left and right sides toward larger-mass center diagonally, straight down along vertical component and across inward along horizontal component. Left and right sides feel slightly less gravity than middle, because they are slightly farther away from larger-mass center. Those particles accelerate downward slightly less than middle does. Left and right sides also accelerate small amount horizontally toward smaller-mass center. This pushes other molecules equally up and down and contributes to vertical stretching out.
waves
Changing gravity changes tidal forces and can cause mass oscillations. Mass accelerations make gravitational waves.
Rotating objects with mass pull space-time around {frame dragging}| {Lense-Thirring effect} {gravitomagnetism}. An analogy is rotating masses drag viscous fluid around them. For particles orbiting around rotating masses, relativity causes orbit-plane precession, because rotation and angular momentum couple.
5-Physics-Relativity-General Relativity
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Date Modified: 2022.0225