Pseudo-Complex General Relativity for Gravitational Waves
P.O.Hess
(ICN-UNAM)
Why pseudo-complex General Relativity
and application to gravitational waves
P.O. Hess,”Alternatives to Einstein’s General Relativity Theory,
Progress in Particle and Nuclear Physics
114
(2020), 103809.
CONTENT
•
INTRODUCTION
•
ALGEBRAIC EXTENSIONS (IN COORDINATES
AND METRICS)
•
SOME PREDICTIONS OF PC-GR: A BRIGHT
RING AROUND A BLÑACK HOLE AND
PROPERTIES OF GRAVITATIONAL WAVES
•
CONCLUSIONS
INTRODUCTION
•
IT IS NOT SURE IF GR IS STILL VALID
IN STRONG GAVITATIONAL FIELDS.
•
PROBLEMS WITH LOSS OF
INFORMATION, QUANTIZATION
EFFECTS, EVENT-HORIZON,
SINGULARITIES, ALL SIGNS THAT
SOMETHING MAYBE MISSING.
•
IN THE PAST SEVERAL ATTEMPTS TO
EXTEND GR HAVE BEEN MADE,
RELATED TO CHANGE THE METRIC
OR THE COORDINATES.
FIRST ATTEMPTS: A ) A. EINSTEIN
Problem:
In the weak field limit the complex part does not approach
the Maxwell equations.
Motivations: To unify GR with Electrodynamics
FIRST ATTEMPTS: B) M. BORN
Motivation: In Quantum Mecanics coordinates and momentum are
treated on equal footing. In GR coordines play the dominant role
ADDING
MAXIMAL ACCELERATION!
Metric in momentum-energy space:
ALGEBRAIC EXTENSIONS
Algebra:
WEAK FIELD LIMIT
with
leads to
ghost solutions
!
Only the pc-extension is save. This is the reason
why to study the pseudo-complex extension
and not others!
a_i**2
C_{ii}PSEUDO-COMPLEX EXTENSION-1
PSEUDO-COMPLEX EXTENSION-2
P.O.Hess, M. Schäfer, W. Greiner: Pseudo-complex General Relativity,
Springer 2015
PC-GR
with
UN MODELO FENOMENOLÓGICO
Due to the non-existence of a theory of quantum gravity:
use phenomenology
Nielsen A., Birnholz O.,AN 2018, 339, 298.
Nielsen A., Birnholz O.,AN 2019, 340, 116.
[
r**6
]
n>3
THE PRINCIPLE BEHIND IS:
A M
ASS NOT ONLY CURVES THE SPACE AS DESCRIBED IN
GENERAL RELATIVITY, BUT ALSO CHANGES THE VACCUM
PROPERTIES AROUND IT (DUE TO QUANTUM EFFECTS),
HAVING IN TURN AN EFFECT ON THE METRIC
Resolution aprox. 20
μ
as
80 degrees inclination, DETAILS
ARE LOST!
Resolution 0.5
μ
as
80 degrees inclination
(a=0.8)
M87
REDSHIFT
•
We cannot tell anything about the property of the Surface
•
How strong te magnetic field can be?, etc.
•
Only infomation about the redshift: Increases toward 90
degrees and with inceasing a, the redshift is decreased
at the poles.
posible observable emision near poles
for rapidly rotating stars, but they are overshine by jets.
From above:
a=0.2m
a=0.5m
a=0.8m
a=1.0m
15
STABILITY OF THE SCHWARZSCHILD SOLUTION
Chandrasekhar’s book; The mathematical theory of black holes
16
THE FIELD EQUATION FOR GRAVITATIONAL
WAVE: AXIEL AND POLAR
m=m(r)!
A rather lengthy, but straight forward derivation leads to:
A NEW ANALYTIC SOLUTION FOR THE
TORTOISE COORDINATE
pc-GR
GR
ASYMPTOTIC BEHAVIOR
TOTAL:
AXIAL MODES:
GR:
pc-GR:
400 iterations
Comaring axial
to polar modes:
Left columna:
axial modes
Right columns:
polar modes
red: 300 iterations
green: 400 iterations
blue: 500 iterations
AN, October (2021), online
CONCLUSIONS:
•
pc-GR is the only viable algebraic extensión of GR (unites ideas with M.
Born and others)
•
pc-GR makes definite predictions:
•
1) A dark ring followed further in by a bright ring in an accretion disk.
Unfortunately, resulution of EHT not Good enough to see it: Hope: future
improvements in the resolution of EHT
•
2) Frequencies of gravitational waves show differences to GR at LARGE
DAMPING. The problema is how to extract these frequencies.
Delve into the concept of pseudo-complex General Relativity (PC-GR) as an alternative theory to Einstein's General Relativity. The study considers algebraic extensions, weak field limits, and the extension of metrics in momentum-energy space. By analyzing predictions and implications, this research sheds light on potential advancements in our understanding of gravitational phenomena.
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Presentation Transcript
Why pseudo-complex General Relativity and application to gravitational waves P.O.Hess (ICN-UNAM) P.O. Hess, Alternatives to Einstein s General RelativityTheory, Progress in Particle and Nuclear Physics 114 (2020), 103809.
CONTENT INTRODUCTION ALGEBRAIC EXTENSIONS (IN COORDINATES AND METRICS) SOME PREDICTIONS OF PC-GR: A BRIGHT RING AROUND A BL ACK HOLE AND PROPERTIES OF GRAVITATIONAL WAVES CONCLUSIONS
INTRODUCTION IT IS NOT SURE IF GR IS STILL VALID IN STRONG GAVITATIONAL FIELDS. PROBLEMS WITH LOSS OF INFORMATION, QUANTIZATION EFFECTS, EVENT-HORIZON, SINGULARITIES, ALL SIGNS THAT SOMETHING MAYBE MISSING. IN THE PAST SEVERALATTEMPTS TO EXTEND GR HAVE BEEN MADE, RELATED TO CHANGE THE METRIC OR THE COORDINATES.
FIRSTATTEMPTS: A ) A. EINSTEIN Motivations: To unify GR with Electrodynamics Problem:In the weak field limit the complex part does not approach the Maxwell equations.
FIRSTATTEMPTS: B) M. BORN Motivation: In Quantum Mecanics coordinates and momentum are treated on equal footing. In GR coordines play the dominant role ADDING Metric in momentum-energy space: MAXIMAL ACCELERATION!
ALGEBRAIC EXTENSIONS Algebra:
WEAK FIELD LIMIT with a_i**2 C_{ii} leads to ghost solutions! Only the pc-extension is save. This is the reason why to study the pseudo-complex extension and not others!
PC-GR P.O.Hess, M. Sch fer, W. Greiner: Pseudo-complex General Relativity, Springer 2015 with
UN MODELO FENOMENOLGICO r**6] [ Due to the non-existence of a theory of quantum gravity: use phenomenology n>3 Nielsen A., Birnholz O.,AN 2018, 339, 298. Nielsen A., Birnholz O.,AN 2019, 340, 116.
THE PRINCIPLE BEHIND IS: A MASS NOT ONLY CURVES THE SPACEAS DESCRIBED IN GENERAL RELATIVITY, BUTALSO CHANGESTHEVACCUM PROPERTIESAROUND IT (DUETO QUANTUM EFFECTS), HAVING IN TURNAN EFFECT ONTHE METRIC
Resolution aprox. 20as 80 degrees inclination, DETAILS ARE LOST! Resolution 0.5 as 80 degrees inclination (a=0.8) M87
REDSHIFT We cannot tell anything about the property of the Surface How strong te magnetic field can be?, etc. Only infomation about the redshift: Increases toward 90 degrees and with inceasing a, the redshift is decreased at the poles. posible observable emision near poles for rapidly rotating stars, but they are overshine by jets. From above: a=0.2m a=0.5m a=0.8m a=1.0m
STABILITY OF THE SCHWARZSCHILD SOLUTION Chandrasekhar s book; The mathematical theory of black holes 15
THE FIELD EQUATION FOR GRAVITATIONAL WAVE: AXIELAND POLAR A rather lengthy, but straight forward derivation leads to: 16 m=m(r)!
A NEW ANALYTIC SOLUTION FOR THE TORTOISE COORDINATE GR pc-GR
ASYMPTOTIC BEHAVIOR TOTAL:
AXIAL MODES: GR: 400 iterations pc-GR:
AN, October (2021), online Comaring axial to polar modes: Left columna: axial modes Right columns: polar modes red: 300 iterations green: 400 iterations blue: 500 iterations
CONCLUSIONS: pc-GR is the only viable algebraic extensi n of GR (unites ideas with M. Born and others) pc-GR makes definite predictions: 1) A dark ring followed further in by a bright ring in an accretion disk. Unfortunately, resulution of EHT not Good enough to see it: Hope: future improvements in the resolution of EHT 2) Frequencies of gravitational waves show differences to GR at LARGE DAMPING. The problema is how to extract these frequencies.
