Mass of Schwarzschild Black Holes Is Indeed Zero And Black Hole Candidates Are Quasi Black Holes.

Abstract

A Schwarzschild Black Hole (BH) is the gravitational field due to a neutral point mass, and it turns out that the gravitational mass of a neutral point mass: $M=0$ (Arnowitt, Deser, Misner, PRL 4, 375, 1960). The same result is also suggested by Janis, Newman, and Winicour (PRL 20, 878, 1968). In 1969, Bel gave an explicit proof that for a Schwarzschild BH, $M=0$ (Bel, JMP 10, 1051, 1969). The same result follows from the fact the timelike geodesic of a test particle would turn null if it would ever arrive at an event horizon (Mitra, FPL, 2000, 2002). Non-occurrrence of trapped surfaces in continued gravitational collapse too demands $M=0$ for black hole (Mitra, Pramana, 73, 615, 2009). Physically, for a point mass at $R=0$, one expects ${\it Ric} \sim M \delta (R=0)$ (Narlikar \& Padmanabhan, Found. Phys., 18, 659, 1988). But the black hole solution is obtained from ${\it Ric} =0$. Again this is the most direct proof that $M=0$ for a Schwarzschild black hole. Implication of this result is that the observed massive black hole candidates are non-singular quasi black holes or black hole mimickers which can possess strong magnetic fields as has been observed. The echoes from LIGO signals, if true, may be the direct evidence that the pertinent compact objects are BH mimickers and not true vacuum BHs.