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Some Aspects of Spacetime Coordinates

Thesis Info

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External Link

Author

Riaz, Syed Muhammad Jawwad

Program

PhD

Institute

National University of Sciences & Technology

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2012

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1018

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727193192

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In this thesis, some aspects of spacetime coordinates are presented. After discussing some non-singular coordinates for the Schwartzschild, the Reissner-Nordstr ̈m and the o Kerr black hole spacetimes, non-singular Kruskal-like coordinates for different cases of general circularly symmetric black holes in (2 + 1) dimensions are constructed. The ap- proach is further extended to construct non-singular coordinates for the rotating BTZ black hole. As Kruskal-like coordinates do not remove the coordinate singularity for the extreme BTZ spacetime geometry, the possibility of obtaining Carter-like coordi- nates is discussed. It is found that these coordinates also do not remove the coordinate singularity for this geometry. The Double-null form has great importance in general relativity (GR), especially in solar-terrestrial relationships, investigation of black hole spacetimes, formulating the Newman-Penrose formalism and Numerical Relativity etc. In Chapter 3, three di- mensional spacetimes are classified according to the possibility of converting them to double-null form. It is found that a class of (2 + 1)−dimensional spacetimes in which coefficient g02 or g12 is non-zero, cannot be transformed to the double-null form. In black hole thermodynamics, it has been shown earlier for different spacetimes that the Einstein field equations at the horizon can be expressed as the first law of black hole thermodynamics. In Chapter 4, a simpler approach, using the concept of folia- tion is developed to obtain such results. Using this simpler approach, thermodynamic identities are established for the Schwarzschild, the Reissner-Nordstr ̈m, the Kerr, and o the Kerr-Newmann black holes. An important aspect of this approach is that one has to essentially deal with an (n − 1)−dimensional induced metric for an n−dimensional spacetime, which significantly simplifies the calculations to obtain such results.
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مغربی تنقید کے اہم نام

موضوع 9:مغربی تنقید کے اہم نام
پس منظر:
لان جائنس کے بعد۱۳۰۰ سال تک خاموشی رہتی ہے اور پھر "دانتے" کے آنے سے یہ خاموشی ٹوٹتی ہے۔انگلستان میں "فلپ سڈنی" ، فرانس کے "بولو"ڈرائیڈن ، پوپ، جانس، گوئٹے، ورڈز ورتھ، کولرج وغیرہ جیسے قابل ذکر نام ہمارے سامنے آتے ہیں۔
ورڈزورتھ:
ورڈز ورتھ کا تعلق انگلینڈ سے تھا۔ اس کی ملاقات کولرج سے ہوئی اور مل کر سوچا جو شاعری ہو رہی ہے اس میں کوئی نئی بات نہیں ہے۔لہذا وقت کی ضرورت ہے کہ انگریزی ادب میں تبدیلی لائیں تاکہ مقصدیت کو بھی ہو۔ لوگوں کو فائدہ بھی ہوگا اس کے لیے ماحول تیار کرنے کی ضرورت ہے۔ ورڈزورتھ نے اپنی کتاب"کلیریکل بلیڈز " کے دوسرے ایڈیشن میں ایک مقدمہ یعنی تمہید لکھی۔جیسے مقدمہ شعر و شاعری میں حالی نے شروع میں جو صفحات لکھے اردو ادب میں ان کو بنیادی اہمیت حاصلہے۔ اسی طریقے سے جو تمہید ورڈزورتھ نے لکھی وہ تنقید کا پورا راستہ متعین کرتی ہے۔اس میں انہوں نے اپنا نکتہ نظر اور ماہیت بیان کی۔ انہوں نے بتایا کہ نئی شاعری کس طرح کی ہونی چاہیئے۔اس کے قواعد و ضوابط کیا ہوں۔ورڈز ورتھ کی تمہید اس اعلان سے شروع ہوتی ہے :
"شاعری بادشاہوں، امیروں اور نوابوں کے لیے نہیں ہے۔اب وہ دور ختم ہوگیا جب اس بات کا خیال رکھا جاتا تھا کہ بادشاہوں کو جو پسند ہے وہ لکھا جائے۔ اب جو موضوعات اور زبان کا معیار ہے وہ لکھا جائے۔اس کے لیے کچھ اصول متعین کیے جانے ہیں۔انہی پر عمل کیا جائے گا۔ اب زبان اور موضوع شاہی دربار سے نکل کر عوام میں واپس آجائے گا۔"
ورڈزورتھ نے جو تھیوری پیش کی اس کا مطلب یہ ہے کہ اب عوام کے لیے لکھیں۔ ورڈزورتھ نے لکھا کہ:
"شاعری اور ادب کا مقصد عام زندگی سے موضوعات حاصل کرکے...

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