Massive scalar field in multiply connected flat spacetimes

Abstract

The vacuum expectation value of the stress-energy tensor 0 |T µν | 0 is calculated in several multiply connected flat spacetimes for a massive scalar field with arbitrary curvature coupling. We find that a nonzero field mass always decreases the magnitude of the energy density in chronology-respecting manifolds such as R 3 × S 1 , R 2 × T 2 , R 1 × T 3 , the Möbius strip, and the Klein bottle. In Grant space, which contains nonchronal regions, whether 0 |T µν | 0 diverges on a chronology horizon or not depends on the field mass. For a sufficiently large mass 0 |T µν | 0 remains finite, and the metric backreaction caused by a massive quantized field may not be large enough to significantly change the Grant space geometry.

Massive spinor fields in flat spacetimes with nontrivial topology

“…The vacuum stress tensor is seen to have the opposite sign, and twice the magnitude of, the scalar stress-energy tensor given in reference [6] (equation (11)). …”

“…The effects of multiple connectedness of the space-time manifolds for massless fields in various topological spaces are studied by Dewitt, Hart and Isham [4]. Following their work, Tanaka and Hiscock [6] evaluated vacuum expectation value of the stress tensor < 0|T µν |0 > for free massive scalar fields in four dimensional space-time manifolds of the type R 1 (time) × Σ(space 3 ).…”

“…It is believed that the gravitational backreaction to these diverging stress-energy tensor would alter the space-time in such a way as to prevent the formation of CTCs. In previous studies [6][7][8][9][10][11][12][13], it has been shown that the divergence of < 0|T µν |0 > for massless scalar fields on various space-times with chronology horizons cannot be generally avoided. Here we will show that the same thing is true for massive spinor field on Misner space.…”

Topology, mass and Casimir energy

“…Casimir-type effects in the presence of massive fields have been studied in [7] and [8] for both scalar and spinor fields. There it has been found that a non-zero field mass always decreases the magnitude of the energy density.…”

Time machines constructed from anti–de Sitter space

“…Hawking thus proposed the chronology protection conjecture which stated that physical laws do not allow the appearance of CTCs [11]. But, many counter-examples to the chronology protection conjecture have been found [12][13][14][15][16][17][18][19][20][21][22]. In particular, Li and Gott [21] have found a self-consistent vacuum for a massless conformally coupled scalar field in Misner space (see also [20]), which gives an example of a time machine (i.e.…”