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Mass–energy emitted as gravitational waves during the most energetic black hole merger observed until 2020 (GW170729) [309] 8.8×10 47 J GRB 080916C – formerly the most powerful gamma-ray burst (GRB) ever recorded – total/true [ 310 ] isotropic energy output estimated at 8.8 × 10 47 joules (8.8 × 10 54 erg), or 4.9 times the Sun's mass ...
Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force. Thus, if the net work is positive, then the particle's kinetic energy increases by the amount of the work. If the net work done is negative, then the particle's kinetic energy decreases by the amount of work. [19]
The Heisenberg uncertainty principle allows the energy to be as large as needed to promote quantum actions for a brief moment of time, even if the average energy is small enough to satisfy relativity and flat space. To cope with disagreements, the vacuum energy is described as a virtual energy potential of positive and negative energy. [93]
Without friction to dissipate a body's energy into heat, the body's energy will trade between potential and (non-thermal) kinetic forms while the total amount remains constant. Any gain of kinetic energy, which occurs when the net force on the body accelerates it to a higher speed, must be accompanied by a loss of potential energy.
While general relativity replaces the scalar gravitational potential of classical physics by a symmetric rank-two tensor, the latter reduces to the former in certain limiting cases. For weak gravitational fields and slow speed relative to the speed of light, the theory's predictions converge on those of Newton's law of universal gravitation. [49]
A contour plot of the effective potential due to gravity and the centrifugal force of a two-body system in a rotating frame of reference. The arrows indicate the downhill gradients of the potential around the five Lagrange points, toward them (red) and away from them (blue). Counterintuitively, the L 4 and L 5 points are the high points of the ...
As can be seen, the mean kinetic and potential energy densities are equal. This is a general property of energy densities of progressive linear waves in a conservative system . [ 22 ] [ 23 ] Adding potential and kinetic contributions, E pot and E kin , the mean energy density per unit horizontal area E of the wave motion is:
The relativistic mass is the sum total quantity of energy in a body or system (divided by c 2).Thus, the mass in the formula = is the relativistic mass. For a particle of non-zero rest mass m moving at a speed relative to the observer, one finds =.