Does Our Universe Live In a Black Hole? Nikodem J. Popławski Department of Physics, Indiana University Bloomington, IN National Institute of Standards and Technology Gaithersburg, MD 29 November 2011

Outline 1. Problems of general relativity and cosmology 2. Solution: gravity with torsion 3. Einstein-Cartan-Sciama-Kibble gravity 4. Big bounce instead of big bang 5. Torsion as alternative to inflation 6. Nonsingular black holes: every black hole as a wormhole to a new universe 7. Torsion as a source of matter-antimatter asymmetry, dark matter, and dark energy

Big-bang cosmology • Albert Einstein (1915) – general theory of relativity • K. Schwarzschild (1916) – exact solution: spherically symmetric gravitational field → black holes • A. Friedman (1922) – exact solution: homogeneous and isotropic Universe → Universe is expanding, Einstein introduces cosmological constant to describe a static Universe • E. Hubble (1929) – observable Universe is expanding

Big-bang cosmology • G. Lemaître (1931) – Universe originated from primeval atom (big bang) • R. Alpher & G. Gamov (1940s) – big-bang (primordial) nucleosynthesis • R. Alpher, R. Herman & G. Gamov (1948) – prediction of cosmic microwave background radiation (CMBR) • A. Penzias & R. Wilson (1964) – discovery of CMBR

Problems of big-bang cosmology • Initial singularity: infinite density • Origin of expansion from extremely hot and dense state? • Horizon problem (1970s): distant regions of Universe have not contacted each other, but they have same temperatures (Universe is isotropic) • R. Dicke (1969) Flatness problem: Universe appears nearly flat at large scales In order for Universe to be nearly flat now, it must have been very flat in past – why?

Inflation Kazanas, Guth, Linde & Steinhardt (1980s) – solution to horizon & flatness problems: cosmic inflation: extremely rapid, exponential expansion of early Universe • Universe started from one causally connected region • Universe was nearly flat before inflation Advantage: predicts observed temperature fluctuations in CMBR Problems of big-bang cosmology with inflation: • Initial singularity unresolved • Need additional assumptions about what causes inflation • Why Universe was nearly flat before inflation? • What ends inflation?

Solution: gravity with torsion? Simplest theory: Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity

What is torsion? • Differentiation of vectors in curved spacetime requires subtracting two vectors at separate points with different geometrical properties • Parallel transport brings one vector to origin of another, so that their subtraction makes sense Change of vector under parallel transport = vector x displacement x affine connection Affine connection is a geometrical property of spacetime

What is torsion? • From affine connection one can construct Curvature – “bending” of spacetime Torsion – “twisting” of spacetime • Spacetime has also metric which measures distances • General relativity (GR): torsion = 0

What is torsion? PHYSICS TODAY

What is torsion? PHYSICS TODAY

Theories of spacetime Special Relativity – flat spacetime (no curvature, no torsion) Variables: matter fields (such as particles, electromagnetism) More degrees of freedom General Relativity – (curvature, no torsion) Variables: matter fields + metric ECSK Gravity (simplest theory with curvature & torsion) Variables: matter fields + metric + torsion

Why ECSK gravity? GR ECSK Intrinsic angular momentum (spin) of matter couples to spacetime NO YES Matter can form singularities YES NO ECSK gravitational repulsion at densities >> nuclear: • Nonsingular black holes • Big bounce instead of big bang • Cosmic inflation not needed

Why ECSK gravity? GR ECSK Dirac equation (describes electrons and quarks, combines quantum mechanics and special relativity) is linear YES NO May explain: • Dark energy • Matter-antimatter asymmetry • Dark matter

Why ECSK gravity? Does this new treatment conflict with what is already known? • Torsion significant only at densities >> nuclear • In vacuum torsion vanishes: ECSK = GR • ECSK passes all current GR tests Is this treatment testable? • Cosmology of very early Universe can test ECSK • Electrons and quarks cannot be point particles in ECSK gravity: spatial structure at 10–25 m

History of torsion Torsion is older than Schrödinger equation • Élie Cartan (1921) torsion • Dennis Sciama and Tom Kibble (1960s) spin produces torsion (energy & momentum produce curvature) T. W. B. Kibble, J. Math. Phys. 2, 212 (1961) D. W. Sciama, Rev. Mod. Phys. 36, 463 (1964) • Trautman, Kopczyński (1970s) torsion may avert cosmological singularities (polarized spins)

History of torsion • Hehl and Datta (1971) Dirac equation with torsion is nonlinear • Hehl and collaborators, Kuchowicz (1970s) torsion induces gravitational repulsion at extremely high densities and averts cosmological singularities (unpolarized spins) → big-bounce cosmology

Big-bounce cosmology • Our Universe was contracting before bounce – from what? Idea: every black hole produces a nonsingular, closed universe Origin of Universe and nature of black-hole interiors are related • Our Universe born in a black hole existing in another universe (Pathria 1972, Smolin 1992) – how? Simplest mechanism – torsion NJP, Phys. Lett. B 694, 181 (2010)

Universe in a black hole

Every black hole forms a new universe Not a resolution

Black holes as Einstein-Rosen bridges

Arrow of time • Why does time flow only in one direction? • Laws of ECKS gravity (and GR) are time-symmetric • Boundary conditions of a universe in a black hole (BH) are not: motion of matter through event horizon (EH) is unidirectional can define arrow of time event horizon future past Information not lost • Arrow of time in the universe fixed by time-asymmetric collapse of matter through EH (before expansion)

How to test that every black hole contains a hidden universe? To boldly go where no one has gone before

Preferred direction • Stars rotate → rotating black holes Universe in a rotating BH inherits its preferred direction NJP, Phys. Lett. B 694, 181 (2010)

Einstein-Cartan-Sciama-Kibble theory of gravity prevents singularities: black hole interiors become new universes

T. Kibble, G. Guralnik, C. Hagen, F. Englert, R. Brout & P. Higgs: relativistic Anderson-Higgs mechanism 2010 APS Sakurai Prize

ECSK gravity Lagrange-Hamilton principle of least action describes most of classical physics • Metric → Einstein equations Curvature = k · (energy-momentum density) • Torsion → Cartan equations Torsion = k · spin density Same coupling constant k

ECSK gravity • Torsion significant above densities For ordinary matter (electrons, quarks) ½ > 1045 kg m-3 Nuclear matter in neutron stars ½ » 1017 kg m-3 Gravitational effects of torsion negligible even for neutron stars Torsion significant only in very early Universe and in black holes

Big bounce from torsion • Friedman equations (Einstein equations for Universe) relate expansion of Universe to energy density and pressure of matter: Universe expands or contracts if energy density ≠ 0 • Spin-torsion coupling produces negative contribution to energy density → gravitational repulsion When total energy density = 0, Universe undergoes a bounce Regular big bounce instead of singular big bang • Universe starts expanding from a finite minimum radius

Cosmology with torsion • After the bounce, Universe very rapidly expands, producing many causally disconnected regions and becoming very flat • Torsion: “fast” growth • Inflation: “large” growth • Rapid expansion caused by extremely strong gravitational repulsion at the bounce • When spin-torsion coupling weakens, Universe smoothly transits from torsion era to radiation-domination era (early Universe) • Unlike inflation, big-bounce cosmology with torsion does not require additional matter fields – advantage of torsion NJP, Phys. Lett. B 694, 181 (2010)

Cosmology with torsion

Black holes with torsion • Where does the mass of Universe come from? Possible solution: stiff matter (speed of sound = speed of light) Ultradense matter (in neutron stars) is stiff • Friedman conservation law for stiff matter → mass of collapsing BH increases (external observers do not see it) • Mass increase occurs via Zel’dovich quantum pair production in strong anisotropic fields Total energy (matter + gravity) remains constant

Black holes with torsion • Particle-antiparticle pairs annihilate to radiation • Radiation isotropizes universe which stops pair production • Gravitational collapse proceeds until the bounce Radius of universe at the bounce – 10-5 m Mass of universe at the bounce – 1062 kg (for a typical BH) NJP, arXiv:1105.6127

Black holes with torsion • After the bounce, universe in BH expands • Spin-torsion coupling introduces matter-antimatter asymmetry which is significant at extremely high densities • This asymmetry results in decay asymmetry • Possible scenario: heavy antifermions in very early Universe decayed into weakly interacting massive particles that form dark matter, while heavy fermions decayed into visible matter Missing antimatter is hidden as dark matter (2000s) NJP, Phys. Rev. D 83, 084033 (2011)

Matter-antimatter asymmetry

Black holes with torsion Expansion to infinity if mass of Universe exceeds Cosmological models with k = 1, ¤ ≠ 0

Dark energy • Quark-to-hadron transition in early Universe and torsion produce a small, positive cosmological constant • Only 105 times larger than observed value • Contribution from leptons could decrease it • Simplest model predicting small, positive cosmological constant – does not use new fields NJP, Annalen Phys. 523, 291 (2011)

Dark energy

Black holes with torsion • Universe in a BH invisible for observers outside (EH formation and everything after occur after infinite time) • As universe in a BH expands to infinity, BH becomes an Einstein- Rosen bridge (Flamm 1916, Weyl 1917, Einstein & Rosen 1935) connecting this (child) universe with the outer (parent) universe Parent universe appears for its child as the only white hole

Black holes with torsion Spherically symmetric, vacuum solutions of GR (& ECSK): • Schwarzschild black hole - singular Final stage of collapse of most massive stars in GR • Schwarzschild white hole - singular Cannot form • Einstein-Rosen bridge (wormhole) - regular Final stage of collapse of most massive stars in ECSK GR & ECSK predict different mathematical solutions as final stages of gravitational collapse of stars ECSK solution is advantageous over GR solution

Summary Thank you! • The Einstein-Cartan-Kibble-Sciama gravity accounts for spin of elementary particles, which equips spacetime with torsion. • For fermionic matter at very high densities, torsion manifests itself as gravitational repulsion that prevents the formation of singularities in black holes and at big bang. • Every black hole produces a new universe inside its event horizon. • Our Universe may be the interior of a black hole existing in another universe. Big bounce instead of big bang. • Torsion solves flatness and horizon problems without inflation. • Nonlinearity of Dirac equation with torsion may explain matter- antimatter asymmetry, dark matter, and dark energy.

Acknowledgments Dr. Chris Cox My Parents: Bożenna Popławska & Janusz Popławski Prof. James Bjorken Dr. Shantanu Desai Prof. Friedrich Hehl Prof. Tom Kibble

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