Abstract
Characterizing black holes by means of classical event horizon is a global concept because it depends on future null infinity. This means, to find black hole region and event horizon requires the notion of the entire spacetime which is a teleological concept. With this as a motivation, we use local approach as a complementary means of characterizing black holes. In this paper we apply Gauss divergence and covariant divergence theorems to compute the fluxes and the divergences of the appropriate null vectors in Vaidya spacetime and thus explicitly determine the existence of trapped and marginally trapped surfaces in its black hole region.
Highlights
The most important predictions of general relativity are Black holes
The study of black holes based on the concept of classical event horizon has the following drawbacks: to locate black hole region and event horizon requires the knowledge of the entire spacetime, the definition does not have direct relation with the notion of strong gravitational field as shown by (Ashtekar and Krishnan, 2004) and (Krishnan, 2012) for example in the Vaidya spacetime, we can have event horizon forming in a flat region
In a dynamical black hole such as the Vaidya spacetime, trapped surfaces are generally located inside the apparent horizon which is found in the event horizon (Ben-Dov, 2007)
Summary
The most important predictions of general relativity are Black holes. They are the spacetime regions from which no signal can be seen by an observer far from the matter sources (Frolov and Zelnikov, 2011). In a dynamical black hole such as the Vaidya spacetime, trapped surfaces are generally located inside the apparent horizon which is found in the event horizon (Ben-Dov, 2007). This is the main result of this paper.
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