Penrose's theorem is more restricted and only holds when matter obeys a stronger energy condition, called the " dominant energy condition ", in which the energy is larger than the pressure.
32.
The most famous classical energy condition is the " weak energy condition "; this asserts that the local energy density, as measured by an observer moving along a time-like world line, is non-negative.
33.
As the expansion gives the rate of change of the logarithm of the area density, this means the event horizon area can never go down, at least classically, assuming the null energy condition.
34.
The most famous classical energy condition is the " weak energy condition "; this asserts that the local energy density, as measured by an observer moving along a time-like world line, is non-negative.
35.
In general relativity, energy conditions are often used ( and required ) in proofs of various important theorems about black holes, such as the no hair theorem or the laws of black hole thermodynamics.
36.
Such matter would violate one or more energy conditions and show some strange properties, stemming from the ambiguity as to whether attraction should refer to force or the oppositely oriented acceleration for negative mass.
37.
The energy condition required for the black-hole singularity theorem is weak : it says that light rays are always focused together by gravity, never drawn apart, and this holds whenever the energy of matter is non-negative.
38.
Rather, relations that hold true for all geodesics, such as the Raychaudhuri equation, and additional non-specific assumptions about the nature of matter ( usually in the form of energy conditions ) are used to derive general results.
39.
All of these are violations of one or another variant of the positive energy condition of Einstein's general theory of relativity; however, the positive energy condition is not a required condition for the mathematical consistency of the theory.
40.
All of these are violations of one or another variant of the positive energy condition of Einstein's general theory of relativity; however, the positive energy condition is not a required condition for the mathematical consistency of the theory.
