1. Awaking the vacuum in relativistic stars: Gravity-induced vacuum dominance Daniel A. Turolla Vanzella Instituto de Física de São Carlos - USP IX Workshop Nova Física no Espaço Campos do Jordão (SP) - 2010 (PhD project of William Couto Corrêa de Lima)

2. Content:  Quantum Field Theory in Curved Spacetimes: an overview  Awaking the vacuum in relativistic stars  The vacuum: structure and consequences  Final remarks  Gravity-induced vacuum dominance

3. The vacuum: structure and consequences  In flat spacetime: - Vacuum fluctuations (virtual pairs) give the vacuum “some” (infinite) energy; Cortesy of Scientific American Brasil - This energy is renormalized to zero (ground level); - Direct observable consequence: Casimir effect;

4.  In flat spacetime: - Vacuum fluctuations (virtual pairs) give the vacuum “some” (infinite) energy; - This energy is renormalized to zero (ground level);  In curved spacetime: - Vacuum fluctuations give the vacuum “some” (infinite) energy; - This energy can be renormalized, but not to zero, in general; - “Observable” consequences: Particle creation in expanding universes; Black hole evaporation; The vacuum: structure and consequences - Direct observable consequence: Casimir effect.... Conceptually, very important... But observationally, very subtle... Why?

5. The vacuum: structure and consequences  In flat spacetime: ħ, c, L  In curved spacetime: ħ, c, G, L, M Is the vacuum bound to be irrelevant in macroscopic systems? (If not zero or infinite)

6. Classical Classical background spacetime ( M, g ab ) + quantized on Field  quantized on ( M, g ab ) ( M, g ab )  Quantum Field Theory in Curved Spacetimes (QFTCS): an overview

7. i. Fix the background metric ii. Solve the field equation for a complete set of positive- and negative-norm modes iii. Expand the field operator using these normal modes, implementing the canonical commutation relations iv. Substitute (formally) the field operator into the classical expression for the energy-momentum tensor and calculate its expectation value (after regularization and renormalization)  Vacuum energy on gravitational fields

8. Gravity-induced vacuum dominance - Field equation: - Background spacetime: - In-modes: - Out-modes: If V out gets sufficiently negative, then is no longer complete! Non-stationary modes:

9. Gravity-induced vacuum dominance  Consequence:...

10. Awaking the vacuum in relativistic stars  Uniform-density compact object:  More realistic neutron stars:

11. Final remarks  Despite the exponential growth, the energy-momentum tensor is covariantly conserved;  How sharp the transition to vacuum dominance is depends on the size of the system: it would take only miliseconds for the vacuum energy density to overcome even the extremely dense matter inside neutron stars;  The vacuum-driven evolution which would then follow (through the semiclassical Einstein equations) awaits to be fully analyzed and may lead to novel (infrared) QFTCS effects.  The idealizations used here (scalar field, asymptotically static spacetime) serve only to illustrate the main idea behind the vacuum-dominance effect without unnecessary complications. The effect may be triggered in much more complicated and realistic scenarios (for instance, with  in non-stationary situations);